Babylonian Astronomy: Editing and Interpreting an Ancient Science

Abstract

The year 1881 marks the birth of Babylonian astronomy as a modern area of scholarship with the first publication about this topic. From the outset, its scholarly practices were based on a variety of methods rooted in Assyriology, astronomy, mathematics and the history of science. In this chapter, the editing practices that were applied to Babylonian astronomical texts and their relationship to research methods in the abovementioned disciplines are traced through the works of the main scholars who were active in the field of Babylonian astronomy between 1881 and 1955. In this period, two phases can be distinguished: a pioneering phase (1881–1935) in which mainly individual tablets were edited while editing practices remained fluid, and a subsequent phase characterized by the appearance of standard editions of complete and coherent corpora of texts. In both phases, the translations and interpretations were strongly shaped by modern mathematics and astronomy.

The research leading to these results has received FUNDING from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant Agreement No. 269804. This chapter was partly written with support from the project “ZODIAC – Ancient Astral Science in Transformation” which is funded by the European Research Council (ERC) under the Horizon 2020 framework (Grant Agreement No. 885478).

For the benefit of the reader, this contribution begins with a very short introduction to Babylonian astral science, its main genres, its chronology and some important concepts that will be mentioned repeatedly. Between 750 BCE and 250 BCE, a host of new genres of astral science emerged in Babylonia. They include astronomical texts, which are mainly concerned with the observation and prediction of celestial phenomena, and astrological texts, which primarily deal with the terrestrial consequences of these phenomena. The largest astronomical corpus, comprising over one thousand tablets, consists of astronomical diaries and related tablets, all written between 650 BCE and 90 CE. Diaries, the most common type, are six-monthly observational reports of astronomical, meteorological, economic and historical data.¹ Also part of this corpus are goal-year texts, almanacs and normal star almanacs, which are compilations of data extracted from diaries for the purpose of prediction.² The underlying predictive method is nowadays referred to as the goal-year method.³ In the fifth century BCE, Babylonians constructed the zodiac by dividing the path of the sun into twelve sections of thirty degrees. This coordinate system was subsequently used for predicting lunar and planetary phenomena in the corpus of mathematical astronomy, which comprises about 450 tablets written between 400 and 50 BCE. Most of these tablets are computed tables, the remainder being procedure texts with instructions on how to compute the tables. The zodiac also underlies various forms of astrology including Babylonian horoscopes, which contain computed planetary positions for the date of birth. For a proper understanding of editing practices in Babylonian astronomy, some knowledge of the sexagesimal place-value notation is also required. In this notation, numbers are represented as sequences of digits, each having a value between zero and fifty-nine. Every digit is associated with a power of sixty that decreases by one in the rightward direction. A special sign is used for indicating vanishing intermediate digits (0). As opposed to our decimal system, which is an absolute notation, the Babylonian notation is relative or floating, because vanishing initials were rarely written and because there is no equivalent of our decimal point. Hence the power of sixty corresponding to each digit can only be inferred from the context.

By limiting the scope of this investigation to astronomical texts, other tablets with astral science edited during or before the same period are disregarded.⁴ This can be justified by the distinct nature of Babylonian astronomy as a scholarly discipline, a consequence of the high mathematical and astronomical complexity of these texts. Since they abound with technical expressions and mathematical computations, they can hardly be translated and interpreted using purely Assyriological methods. This is particularly true for the tabular texts of mathematical astronomy, which contain little more than sequences of sexagesimal numbers. In fact, these tablets can, to a large extent, be translated and analyzed without any knowledge of the Akkadian language. Not surprisingly, Babylonian astronomy became the domain of scholars who were relative outsiders to Oriental studies, being primarily trained in modern mathematics and astronomy. Their distinct educational and professional background shaped the editions and interpretations of the astronomical texts. For reasons of space, the investigation is also limited to the most important scholars, which leaves out several scholars who occasionally worked on this topic.⁵ Furthermore, this chapter is not concerned with Babylonian astronomy itself, the history of its reconstruction or the biographies of the involved scholars. For the latter two aspects, the reader is referred to de Jong (2016), who covers the same time period and, by and large, the same scholars. A brief outlook on developments after 1955 concludes this chapter.

Editing practices are traced here through a selection of exemplary astronomical tablets, labeled T1–T4. Most of them were edited multiple times, usually because a new fragment was found or progress was made with the astronomical interpretation. All four are kept in the British Museum and belong to what is nowadays referred to as the Babylon collection. The approximately 20,000 tablets of this collection were excavated unscientifically between 1876 and the 1880s and acquired through explorers and antiquities dealers. Only decades later, it became clear that the astronomical and many other tablets in this collection largely originated from Babylon. In order to aid the reader, some guidance to the confusing nomenclature of the tablets seems warranted.⁶ Originally, each group of tablets within the Babylon collection was identified by a date (e.g. 81–7–6 = 7 June 1881) or the name of the individual through whom it was acquired (e.g. Rm = Rassam, SH = Shemtob, Sp = Spartoli). For some groups of tablets, both types of labels were in use (e.g. 76–11–17 and S+, or 81–7–6 and SH).⁷ Individual tablets within each group are identified by a running number (e.g. 81–7–6, 277). At a later stage, a single running British Museum (BM) number was assigned to each fragment, which is how they are usually referred to in modern publications. Text T1 is a tabular text from the corpus of mathematical astronomy. In modern terms it is classified as a synodic table of lunar System B.⁸ The editions of its fragments cover the entire history of research on Babylonian astronomy. Text T2 is a normal star almanac, a predictive compilation of data drawn from astronomical diaries. Text T3 is a procedure text for lunar System A. Text T4 is another procedure text concerned with Jupiter System A’. The following table lists all the major publications on these tablets, including the latest editions.

	Publication	(Partial) edition of
T1	Epping and Strassmaier (1881: 283–286)	81–7–6, 277
	Epping (1889: 8–16, Appendix)	81–7–6, 277 (‘A’) and 81–7–6, 272 (‘C’)
	Epping (1890: 225–240, Appendix)	81–7–6, 277 (‘A’)
	Kugler (1900: 9–16)	Sp 2, 52 + 759 + 81–7–6, 272 + 277 + 331 + 333 + 386 + 589 (‘no. 272’)
	Schaumberger (1935: 375–394, Plates XV–XVII)	BM 34580 + BM 42690 = Sp 2, 52 + 75 + 81–7–6, 272 + 277 + 331 + 333 + 386 + 589 (‘BM 34580’)
	Neugebauer (1936)	review of Schaumberger (1935)
	Pinches and Sachs (1955: No. 66)	Copy of BM 34580 + BM 42690
	Neugebauer (1955: No. 122)	BM 34580 + BM 42690
	Steele (2010: Text G)	BM 34580 + BM 42690 + BM 42869 + BM 42902 + BM 43000 + BM 43030
T2	Epping and Strassmaier (1881: 287–289)	Discussion of Sp 129
	Epping (1889: 152–159, Plates 1–3)	Sp 129, including copy
	Hunger (2014: No. 87)	BM 34033 (Sp 129)
T3	Kugler (1900: 59, 66–67, 72–73, 76, 78–79, 116, 142–147, 160–165, 169–173, 180–181, 191–192)	BM 32651 (‘S+ 2418’)
	Neugebauer (1955: Nos. 200 and 200aa)	BM 32651 and BM 32172
	Ossendrijver (2012: No. 53)	BM 32167 + BM 32172 + BM 32451 + BM 32651 + BM 32663 + BM 32744 + BM 32752
T4	Kugler (1907: 136–140, Plate XVI)	BM 33869 (Rm 4, 431)
	Neugebauer (1955: No. 810)	BM 33869
	Ossendrijver (2012: No. 32)	BM 33869

Until 1881, little more was known about Babylonian astronomy than what was compiled from scattered passages about Chaldeans in the works of Greek and Roman scholars.¹⁰ However, they reveal almost nothing substantial about Babylonian methods and practices. The appearance in 1881 of a pioneering paper by Epping and Strassmaier about newly discovered Babylonian astronomical tablets kept in the British Museum marks the beginning of modern research on Babylonian astronomy. The history of this field may be divided into three phases.¹¹ The first phase (1881–1935) began with the pioneering works of Epping and Strassmaier, culminating in the monumental volumes of Franz Xaver Kugler. Throughout this phase, individual tablets were edited, often only partially, while editing practices remained fluid. The main interest of these scholars was to reconstruct the Babylonian astronomical methods. The following phase (1935–1986) is characterized by the appearance of standard editions of complete and coherent corpora of texts. Otto Neugebauer was the dominant scholar, with significant contributions by Abraham Sachs, Bartel van der Waerden and several other scholars. The translations and interpretations were strongly shaped by modern mathematics and astronomy. The beginning of a third phase characterized by a more holistic, contextualizing approach to Babylonian astral science can be dated to about 1986.

1 Epping and Strassmaier

Babylonian astronomy was rediscovered in 1880 by the orientalist Johann Nepomuk Strassmaier (1846–1920) and the astronomer Joseph Epping (1835–1894), German priests of the Jesuit order (Societas Jesu).¹² Strassmaier knew Epping from the time when he studied theology and philology at the Jesuit Collegium Magnum in Maria Laach, where Epping taught mathematics and physics. Like many Jesuits, Strassmaier left Germany in 1872 when the order was banned by Bismarck. From 1878 onwards, he spent much of his time in the British Museum, studying cuneiform tablets as they were arriving.¹³ In 1880, while visiting the philosophical seminary of the German Jesuits in castle Bleijenbeek (the Netherlands), Strassmaier mentioned the existence of astronomical tablets to Epping, suggesting a collaborative project in order to decipher them. In 1881, this resulted in a publication titled Zur Entzifferung der astronomischen Tafeln der Chaldäer (On the Decipherment of the Astronomical Tablets of the Chaldeans),¹⁴ the first of several papers on this topic to appear in Stimmen aus Maria-Laach (Voices from Maria Laach). This scholarly journal of the German Jesuits was founded essentially as a platform to counteract the increasing attempts by liberals, nationalists and socialists to reduce the role of Catholicism in German public and intellectual life.¹⁵ However, not all contributions have an apologetic tone and they cover a wide range of topics including ancient and modern history, church history, literature, theology, philosophy, education, contemporary social, political and ethical issues and, more rarely, the natural sciences. History of astronomy was an exceptional topic in the journal,¹⁶ but astronomy was a major focus of Jesuit scholarship during the nineteenth century and early twentieth century. Jesuits founded numerous observatories across the globe in order to promote astronomy and, by implication, a new societal role for the Catholic church as a sponsor of modern science and education (Udías 2003, 2015). Epping was actively involved in these endeavors, having taught mathematics and astronomy along with other Jesuits at the newly founded polytechnic school and observatory in Quito, Ecuador, from 1872 to 1876 (de Jong 2016; Udías 2015: 149–150, 218). At the same time, Assyriology was gaining prominence as a matter of public and scholarly debate in Germany (see below). Against this background, Jesuits could justifiably consider Babylonian astronomy to be an appropriate and promising area of scholarship. However, the writings of Strassmaier and Epping reveal almost nothing about such considerations. For a recent discussion of their 1881 paper and a selection of translated passages the reader is referred to de Jong (2016: 269–272). Here it suffice to summarize some important features of their approach to the problem of editing and interpreting the newly discovered Babylonian astronomical tablets. The paper consists of a five-page historical introduction in which Strassmaier reports on the current state of knowledge of ‘Chaldean astronomy’—the term commonly used in this era for Mesopotamian astral science. For him, these texts are mainly of interest because he believes that they will provide a solid basis for understanding the Babylonian calendar and other aspects of ancient chronology. In that view, the recently found Assyrian tablets from Kuyuncik (ancient Nineveh) published by the French-German orientalist Jules Oppert (1825–1905) and the British Assyriologist Archibald Sayce (1845–1933) add only little to the sparse information drawn from classical sources, since they mainly deal with celestial omens (‘portents’)¹⁷:

The largest part of the texts which the mentioned scholars [Oppert and Sayce] used for their works are so-called tablets of portents, which on many occasions give the astrological significance of constellations, usually in a rather incomprehensible manner and, as far as we can judge, without any interest (Epping and Strassmaier 1881: 279).

Apart from mentioning classical sources about Chaldeans, neither Strassmaier nor Epping makes an effort to position their research in the wider history of science. When Strassmaier turns to the astronomical tablets from Babylonia,¹⁸ he stresses how difficult it is to read these often fragmentary and cursively written pieces of unburnt clay, and how important it is to copy them, before they eventually disintegrate (Epping and Strassmaier 1881, 280–281; de Jong 2016, 269). The remaining ten pages, entitled ʻAstronomical Revelationsʼ [Astronomische Enthüllungen], were written by Epping. After humbly conveying his initial doubts about his own competence, claiming, for instance,¹⁹

I did not believe I was a computer sufficiently skilled to solve an equation with so many unknowns and so few knowns…,

Epping reports that he was thrilled to contribute to the project by using his astronomical knowledge. It is interesting to note that Epping here uses the mathematical metaphor of solving an equation with many unknowns in order to characterize the problem of deciphering and interpreting the astronomical tablets. He was also the first scholar to use modern equations for analyzing Babylonian astronomical tables (see below). Epping continues with a classification of the tablets into a computational, an observational and an intermediate category²⁰:

Among the tablets that were available to me, a twofold kind could immediately be distinguished: computational and observational tablets; a third kind probably constituted the key to both. If the latter were deciphered one would, of course, have a great tool for clarifying the remaining ones; but that was a matter of the learned gentlemen Assyriologists. However, as long as they were unable to dispel the darkness, the other road had to be taken on the astronomical side; first the other tablets were to be understood and then it might be possible to draw conclusions for the explanatory tablets. Easier things first is a recognized practice; those tablets that contained almost only numbers had to constitute the first object of attack. In some of them one could discover a constant difference between the subsequent numbers; hence they formed a so-called arithmetical progression, analogous to the usual number sequence. From that, this sequence of numbers thus obtained is used for deriving from it another one, and from the latter a third one. The tablet available to me proceeds until the formation of a third-order difference sequence.

The first category concerns tablets now classified as mathematical astronomy; the second one concerns a normal star almanac. It is not fully clear what kind of tablets gave rise to the third category. Epping’s background as an astronomer is obvious from his preference for the numerical tables. He then presents results of his investigations of two tablets, including a partial edition of the reverse of fragment 81–7–6, 277 (T1). Of the seven partly preserved columns of numbers, nowadays referred to as Ψ”, F, G, H, J, K and L of lunar System B, Epping edits and discusses only K and L, which he calls A and B. Strassmaier’s copy is not included, nor are any details provided about it, but there is no doubt that Epping used the copy shown in Fig. 14.1.²¹

Fig. 14.1

Left: Strassmaier’s unpublished partial copy of the reverse of 81–7–6, 277 (T1) dated 3 June 1879. Right: translation by Epping and Strassmaier (1881)

By choosing capital letters as labels for the columns, Epping initiated a convention used by all subsequent scholars. With Epping, they still have a double role, namely to indicate the position of the column on the fragment and, secondly, to serve as a purely conventional modern symbol for the quantity tabulated in the column.²² As we shall see, Epping also used these symbols for expressing mathematical relations between the columns in modern formulas.²³ Sexagesimal numbers are represented by Epping in tabular form, with each digit vertically aligned in its own subcolumn separated from the next one by a vertical ruling. This formatting of the digits reflects Epping’s essentially correct understanding of the underlying algorithm, but no strict alignment is apparent in Strassmaier’s copy or in the cuneiform original. The dash is used as a distinct symbol for vanishing final digits, but these digits are not written, as can be seen for instance in Column A, lines 5–6, 9. Sexagesimal numbers are translated using a relative notation as in the original (i.e. they do not include any markers of the power of sixty that corresponds to each digit; e.g. the number 2 41 40 10 in Column A). Only in the commentary does Epping explain that the first digit of A and B represents the number of ‘hours’, where one ‘hour’ corresponds to one-sixth of a day.²⁴ The translation is followed by a critical apparatus to which the reader is directed by asterisks (*). Epping’s reconstruction of the algorithmic connection between A and B prompted him to correct some of the numbers copied by Strassmaier. In his words: ‘the numbers designated with stars are improvements of the copy; perhaps the original is damaged there.’ (Epping and Strassmaier 1881, 284, footnote 1).²⁵ The following numbers are provided with an asterisk:

(A10), 48	Epping changes Strassmaier’s 28 to 48, which is the correct reading (the 20 is in fact a crammed 40). However, Strassmaier’s copy offers no clue that the 20 might be read differently.
(A12), 40	Strassmaier copied a 50, which is the correct reading. Epping changed it to 40 on the basis of the entry in B12, using the algorithmic connection between A and B, but the number in B12, 2 21 45 40, was wrongly copied by Strassmaier. The actual number on the tablet is 2 31 45 40, consistent with the 50 in A12.
(A13), 26 54	Strassmaier correctly copied 35 3, which Epping changed to 26 54 on the basis of the entries in B12–13, again using the algorithmic connection between A and B, but these numbers contain errors.
(B2), 5	Epping changed Strassmaier’s 2 to a 5. Again, Epping inferred this correction from the algorithmic connection between A and B. Indeed the tablet has a 5 that was wrongly copied as a 2 by Strassmaier.

Each asterisk correctly identifies a problem in the text as copied by Strassmaier. However, nothing in Strassmaier’s copy indicates that any of these readings are doubtful. Epping expresses the relation between columns A and B in the modern formula B_n–1 + A_n = B_n, where n labels the month, corresponding to row n in the table (i.e. the value of B in row n is obtained by adding the value of A in that row to the value of B in the previous row (n – 1). Already with Epping, modern mathematical equations had become a tool for representing and analyzing Babylonian astronomical algorithms.²⁶ In this, he was followed by all subsequent researchers. Epping also provides an essentially correct astronomical interpretation of A and B.

The paper continues with a discussion of Sp 129 (T2), a tablet now classified as a normal star almanac. Epping provides a lively account of his efforts to understand its content by comparing the reported data with his own astronomical computations for the year 123 BCE, but he refrains from editing the text²⁷:

In the meantime, we now turn to the other category of tablets, that is, those on which observations are reported. This is where the real difficulty begins… In the running text, some expressions could be identified with more or less certainty; thus, to list the most important ones: dil-bat Venus, gut-tu Jupiter, ū (ammatu) cubit or degree, attalu eclipse, an (kakkabu) star, same heaven, si (namir) visible, bir (nûru) glow and some others of lesser significance… The fruitless computations lasted until the third Sunday after Easter, the Feast of St. Joseph. Then I wanted to have a last try. And having begun the work, suddenly the thought came to me: why are you so possessed with the fatal guttu = Jupiter? Try guttu = Mars. Thought, done… In the meantime, my honored brother P. Strassmaier, whom I had immediately informed about my finding, surprised me with an extremely valuable present. As he saw that the investigation had been directed into better waters, he immediately set out to copy the entire tablet of the year 123 once more with the utmost accuracy and render it pronounceable for me in Latin letters.¹ … The new copy was indeed Classical; everything was much clearer now. [Footnote 1:] Copying is no futility: apart from a great aptitude, it requires unusual combinatorial sharpness of mind. If a certain philological tact is lacking then one will separate signs that belong together and, conversely, join the wrong ones.

As becomes clear from this passage, even basic astronomical terms like the names of planets were not yet clarified,²⁸ which explains why Epping and Strassmaier chose not to offer a translation. Epping concludes by stating that ‘Assyriology has opened up a fruitful field of activity for astronomy.’ (Epping and Strassmaier 1881: 291).²⁹ In other words, he envisions Babylonian astronomy as a field of scholarship not only for Assyriologists, but also for astronomers.

In the following years, Epping and Strassmaier collaborated on their project in Bleijenbeek Castle (the Netherlands), until Strassmaier returned to London in 1884. In 1889, their results appeared as a 200-page supplement to the Stimmen aus Maria Laach entitled Astronomisches aus Babylon oder das Wissen der Chaldäer über den gestirnten Himmel (Astronomy from Babylon or the Chaldean Knowledge of the Starry Sky). In this impressive monograph, an enormous step forward is made in reconstructing the Babylonian astronomical methods and, to some extent, also in editing practices. While Epping wrote the astronomical chapters, Strassmaier contributed an introduction and several Assyriological appendices with transliterations, copies and a glossary. Epping’s style is deductive and remarkably informal. Rather than systematically arranging their final results, he presents a lively chronological narrative with insights, mistakes and anecdotes. Apart from reflecting his personality, he may have considered this style to be appropriate for drawing the attention of his fellow Jesuits to an unusual topic. As in 1881, mathematical astronomy has his priority. The reverse of the lunar table 81–7–6, 277 (T1) is now edited more completely. An additional fragment, 81–7–6, 272 (‘Tablet C’), physically joins it, but Epping does not report this until we get to page 101. Both are rendered in a tabular format, with some logograms given in transliteration, while other signs are translated. In particular, the month names are translated with Hebrew equivalents – a practice that remained common well into the twentieth century. Logograms of which the Akkadian reading was unknown are transliterated, using the conventions of his time (bar, sik, num, tab, lal, šu).³⁰ If a logogram is repeated in subsequent rows, Epping uses an abbreviation for this („). Several explanatory columns with modern data are inserted between the Babylonian columns. In Epping’s words³¹:

The Columns a, b, c₁, c₂, d, etc. were copied in the order in which they were found on the cuneiform tablets, but the ones marked x, y, v were added for clarity and comparison, of which x determines the horizontal row, y the number of days which the month written next to it should contain according to the computation and, finally, v represents the row e in accordance with our division of the day into 24 hours.

Epping now edits all but one of the columns, independent of whether or not he understood their computation.³² He introduced a new set of symbols for them, such that d and e correspond to A and B in the 1881 paper. The explanatory columns (x, y, v) are typographically indistinguishable from the other columns. On the other hand, Epping has become more hesitant to correct Strassmaier’s readings if they do not match his expectations. For instance, numbers which he had modified in 1881 (Fig. 14.1) are now maintained and qualified by the remark undeutl. (uncl.) (Fig. 14.2). Epping does not explain these changes, but they seem to reflect his developing understanding of the transliteration as a more or less objective representation of what is legible on the tablet as opposed to what should have been there according to his reconstructions. On Page 101 Epping returns to the tablet, remarking that the fragment 81–7–6, 272 (‘Tablet C’) must join it on the right side. The following remarks, placed next to the translation of ‘Tablet A’ (Fig. 14.2), also suggest an increased sensitivity to the original sources³³:

These three tablets are located in the British Museum, in particular A and C in the collection of Shemtob, B in the collection of Spartoli, but they were not numbered when they were copied in 1879 and could not be collated anymore, since the assistant Th. G. Pinches could no longer find the same. The upper line in eA is an addition for later use, computed from rules. In eB, I and II are erroneous and illegible in the original, they have been reconstructed from rules.

Here, eA stands for Column e of Tablet A, eB for Column e of Tablet B, and the Roman numerals refer to line numbers.

Fig. 14.2

Epping (1889): translation of the reverse of 81–7–6, 277 (‘Tablet A’) and 81–7–6, 272 (‘Tablet C’). Modern equivalents of Epping’s designations: a = F, b = G, c₁ = H, c₂ = J, d = K, e = L, m = M, g = N, h = O, i = NA₁, k = KUR

Chapters 3 and 4 are dedicated to ‘ephemerides’, Epping’s term for almanacs, normal star almanacs and other compilations related to the astronomical diaries. In a paragraph titled Realübersetzung mit Text in Transcription (Factual translation with text in transcription), we find an edition of Sp 129 (T2) (Epping 1889: 152–159, Chap. 4, §10). Epping explains the purpose of his ‘factual translation’ as follows³⁴:

The aim of the following factual [sachlich] translation is to represent the concrete meaning of the cuneiform signs insofar as they signify identical phenomena. However, meanings that are already known from Assyriology or made probable in the present investigation have also been put to use. For the month Nisan the lunar dates have also been added in the translation.

The edition includes, in this order and on facing pages, a translation and a transliteration (called ‘transcription’), while the copy is placed in an appendix. This is the earliest edition of a Babylonian astronomical text to include all three representations. Note that the format commonly used in other branches of Assyriology in the nineteenth and early twentieth centuries, with alternating lines of printed cuneiform text, transliteration and translation,³⁵ was never adopted for editions of Babylonian astronomical texts, most likely because of the mentioned problems of transliteration and translation. The transcription by Epping and Strassmaier consists mainly of normalized Akkadian words with some transliterated signs, sometimes followed by a normalization in brackets, all in the same font. Signs for which the Akkadian reading is uncertain are transliterated in a cursive font, damaged or missing signs are rendered by dots, as can be seen in the first section for the month Nisannu³⁶:

Compared to the terse, technical formulation of the Babylonian original, the ‘factual translation’ is rather free and verbose. Signs and phrases whose meaning could not be established are omitted from the translation without any typographical markers (Fig. 14.3). Epping’s remarks on the ‘factual translation’ can therefore be taken to mean that he primarily aims to render the effective, technical meaning of the cuneiform signs inferred through his astronomical and mathematical interpretations, with a lesser role for meanings established by philological means or established in other domains of Assyriology.

Fig. 14.3

Transliteration and ‘factual translation’ of the first section of T2 in Epping (1889)

The monograph was followed in 1890 by a short paper with new results on text T1 accompanied by an edition in tabular format similar to the previous one, except that the rightmost column (m) is omitted and one more explanatory column is added. The transliterated signs tab (‘add’) and lal (‘subtract’) in Column c₂ (nowadays: J) are replaced by the symbols + and –, and the sexagesimal numbers in Columns a–e are expressed in an absolute notation with modern symbols for degrees, minutes and seconds of arc attached to the first number in each column.³⁷ This paper is the first publication on Babylonian astronomy to contain a graphical representation of the zigzag algorithm (Fig. 14.4), referred to by Epping as ‘gebrochene Differenzreihe erster Ordnung’ (broken first-order difference sequence).³⁸ Epping included the figure ‘um ein Bild von der babylonischen Annäherung zu gewinnen (in order to gain an impression of the Babylonian approximation) (i.e. in order to assess visually how well b approximates the empirical value of the quantity it aims to describe, which he identified, essentially correctly, as the mean synodic month).³⁹ The objective of assessing how accurately an ancient algorithm reproduces empirical behavior is clearly rooted in Epping’s professional background as an astronomer and was later also pursued by other scholars of Babylonian astronomy with a similar background. As we shall see, Kugler refrained from including modern graphs of Babylonian algorithms, but with Neugebauer, they became a common feature in any work on Babylonian astronomy.

Fig. 14.4

Graph from Epping (1890) with the zigzag curve for ‘Column b’ (nowadays: G) and a corresponding modern curve for the duration of the mean synodic month

In Epping’s time, Assyriology was a young discipline lacking firmly established conventions and channels of publication. Editing practices were fluid to the extent that transliteration and translation were sometimes combined in a single representation and restored text was not always distinguishable from preserved text. Little attention was paid to a tablet’s physical features and archaeological context. However, in the late 1880s, Assyriology was consolidating its position in the academic world with the founding of several disciplinary journals (e.g. Revue d’Assyriologie (1884) and Zeitschrift für Assyriologie (1886)). Epping’s 1890 paper was his last one on Babylonian astronomy to appear in the Stimmen aus Maria Laach.⁴⁰ Between 1890 and 1893, Epping and Strassmaier published several further papers on Babylonian astronomy in the Zeitschrift für Assyriologie. In the latter papers, their editing practices have advanced considerably, which presumably reflects the different standards and readership of this journal. For instance, their edition of a Goal-Year text (Epping and Strassmaier 1891) is arranged in two columns, of which the left one contains a transliteration and the right one a translation.⁴¹

Ever since the pioneering years of Strassmaier and Epping, the integration of Assyriological and astronomical competences has been a central and often problematic issue for scholars of Babylonian astronomy. As we shall see, Franz Xaver Kugler strongly felt that one should master both, clearly in response to the strict division of these competences that existed between Strassmaier and Epping. Even though he and later scholars such as Otto Neugebauer did acquire significant Assyriological competences, the traces of their original profession in the natural sciences and mathematics can hardly be overlooked in their works.

2 Franz Xaver Kugler

Franz Xaver Kugler (1862–1929) studied chemistry in Munich and received a PhD in that field from the University of Basel in 1885. After entering the Jesuit order in 1886, he studied philosophy and theology at Jesuit colleges in the Netherlands and England. From 1894 until his death in 1929, he taught mathematics at the German Jesuit college then located in Valkenburg (the Netherlands). By 1897, he followed in the footsteps of Epping. Before exploring Kugler’s editing practices, it is worth noting that he emerged as a scholar of Babylonian astronomy exactly when Near Eastern studies were undergoing a spectacular development in Germany. In 1899, the Deutsche Orientgesellschaft was established, under whose auspices Robert Koldewey began his excavations in Babylon in 1900. That same year Friedrich Delitzsch was installed as professor of Assyriology at the Friedrich-Wilhem University (now Humboldt University) in Berlin. Three widely disseminated public lectures held by Delitzsch in 1899–1901 mark the beginning of the era of Pan-Babylonism, a school of thought in which Judaism and Christianity were viewed as deeply dependent on Mesopotamian precursors.⁴² Some Panbabylonists construed their theories around the notion of an ancient Mesopotamian astral cult.⁴³ It is primarily the efforts of these scholars to prove a very old age of Babylonian astronomy that were attacked by Kugler. In several publications, he used his profound knowledge of the astronomical texts to demonstrate conclusively, often with cynical disdain for his opponents, that Babylonian astronomy did not emerge before the first millennium BCE .⁴⁴

Already in 1900, Kugler published an impressive monograph titled Babylonische Mondrechnung. Zwei Systeme der Chaldäer über den Lauf des Mondes und der Sonne (BMR) (Babylonian Lunar Computus. Two Systems of the Chaldaeans Concerning the Course of the Moon and the Sun). A novel feature of this work is that it deals with a single, coherent group of texts from the corpus of mathematical astronomy. The observational tablets were to be dealt with in a separate publication. Kugler is the first scholar of Babylonian astronomy to use the term ‘critical edition’. In this connection, he issues a disclaimer in the introduction, because he considers himself to be incapable of producing one⁴⁵:

That the following investigations are primarily of a mathematical-astronomical nature is obvious; however, the hope is not unfounded that also the Assyriologist will find something in them not unworthy of his attention – even though the form in which it is presented may contain several flaws… The cuneiform tablets included in the book were reproduced from the copies of Strassmaier. Even if my less practiced hand could not mimic the clear, recognizable features of the experienced master, all cuneiform signs are correct and they wholly serve their purpose, which is twofold. First of all, these cuneiform texts are the only basis of the present investigations and therefore the reader of the latter has the right to view the former. That is not only appropriate but even necessary, since without the cuneiform text being available, certain arguments of the author are not comprehensible at all and, moreover, several cuneiform signs could only be provisionally transcribed and will need to be rectified later by someone competent. Therefore, a critical text edition [kritische Textausgabe] is not intended at all; only by the present work will such become possible, and it also requires a careful collation with the original in the British Museum. But even in this form the copies of Strassmaier yield all that is required for a profitable investigation [gedeihliche Bearbeitung]. On several locations changes had nevertheless to be made in the transcription; but, apart from the fact that this usually concerns damaged parts, the error may be sought on the side of the Chaldean copyist or that of the palaeographer.

These reflections on editing methods reveal that Kugler’s Assyriological scholarship was more developed than that of Epping, to the extent that he was rather critical of Strassmaier’s achievements.⁴⁶ Nevertheless, Kugler continued to rely on his copies and, as far as known, he never copied or collated a cuneiform tablet himself. He also displayed the same tendency as Epping to ‘correct’ Strassmaier’s copies if his reconstructions of the astronomical algorithms appeared to require it, blaming the error on the ‘Chaldean copyist or that of the palaeographer’ (i.e. Strassmaier). In BMR, which comprises 215 pages and thirteen appendices, Kugler discusses a dozen tablets, including the ones previously analyzed by Epping and Strassmaier. Instead of Epping’s informal style, Kugler’s writing is more strongly guided by systematic considerations. For instance, he begins (Kugler 1900: 1–8) by introducing the term ‘system’ —the set of algorithms underlying a group of tables, a central concept in all subsequent historiography on Babylonian mathematical astronomy. He identifies two of them, which he labels I and II, corresponding to B and A in the modern terminology. The systematic approach permeates the entire monograph which is divided into three parts⁴⁷ further subdivided into sections, each of which typically deals with one column and the algorithm reconstructed from it. Like Epping, Kugler uses modern formulas for representing Babylonian algorithms but, unlike Epping, he refrains from including modern graphs of them: the few graphs that are contained in BMR are concerned with modern astronomical computations.

Kugler’s new edition of T1 begins with a description of the physical characteristics of the tablet and a discussion of previous research (Kugler (1900: 9–16).⁴⁸ He correctly identifies the word tersitu, which appears in the colophon as the Babylonian term for this kind of astronomical table. Although it is the first edition of T1 to cover both sides of the tablet (Fig. 14.5), it is nevertheless incomplete, because Kugler omits the columns beyond L, which are contained on the fragment 81–7–6, 272 (Epping’s ‘Tablet C’). He also omits Strassmaier’s copy of the tablet, which was published much later by Schaumberger (1935). Kugler’s understanding of the algorithms for A–L enables him to restore any missing number in these columns. These restorations are printed in a cursive letter of smaller size, as explained in a footnote (Fig. 14.5), but otherwise not marked. His editing practice also differs from the modern one in that signs of which the Akkadian reading was unclear are rendered in transliteration (the logograms tab, lal, sik, bar, num),⁴⁹ other signs are rendered in normalized Akkadian (the month names) and still others in translation (the zodiacal signs). Like Epping, Kugler separates the digits of the sexagesimal numbers by small spaces and he strictly aligns them; the latter feature is not apparent in Strassmaier’s copy or on the original tablets. Moreover, he adds horizontal rulings in order to mark the extrema in each column, such that a single ruling indicates a minimum and a double one a maximum (Fig. 14.5). This convention, which was later adopted by O. Neugebauer (1955) in Astronomical Cuneiform Texts (ACT) (see below), has no counterpart on the tablets either. The edition is followed by a detailed analysis of the columns (Kugler 1900:16–40, 88–114). Kugler introduced his own nomenclature for the columns based on capital letters, which was later slighthly modified by Neugebauer.

Fig. 14.5

Partial edition of T1 in Kugler (1900: 12–13)

In Part III, which deals with lunar ‘System II’ (nowadays: A), Kugler includes a nearly complete edition of the Lehrtablet (instructional tablet) S+ 2418 (T3), the first ever edition of a procedure text of mathematical astronomy. It is not edited as a coherent text but carved up into individual procedures, each edited in a different paragraph. This approach is a consequence of the rigorous systematic structure that Kugler imposed on his monograph. Note that he was later followed in this by Neugebauer, who split up the procedure texts along similar lines in ACT (see below). Kugler considered this text to be of great importance for reconstructing ‘System II’, as is apparent from the following statement in the introduction to Part III⁵⁰:

The instructional tablet S+ 2418 which was mentioned and utilized earlier offers a comforting confirmation of our conjectures and computations, while, on the other hand, the number columns of the lunar tables help to uncover the meaning of the technical expressions of that tablet, which would otherwise remain wrapped in eternal darkness (Kugler 1900: 116).

A revealing example of Kugler’s approach is his edition of the procedure for ‘Column G’ (nowadays: F), which he correctly interprets as the moon’s daily displacement along the ecliptic.⁵¹ The edition consists of a transliteration (Fig. 14.6), a ‘factual translation’ [Realübersetzung] (Fig. 14.7) and a ‘justification of the preceding translation’.⁵²

Fig. 14.6

Selected lines from Kugler’s transliteration of the procedure for ‘G’ (=F) in T3 (Kugler 1900)

Fig. 14.7

‘Factual translation’ of the transliterated text from Fig. 14.6 (Kugler 1900: 160).

Whenever Kugler feels confident about the Akkadian reading of an expression, he puts this into the transliteration. Another difference with modern editing practices concerns the transliteration of logograms, called Wortzeichen (word signs) by Kugler. Even though the Sumerian origin of the logograms was quite well understood by 1900, Kugler avoids this issue and he does not make a typographical distinction between ‘word signs’ and Akkadian phonetic signs. By 1907, when Book I of Sternkunde und Sterndienst in Babel (SSB) (Kugler 1907) appeared, Kugler had sorted out these things (see below).

The term ‘factual translation’ was also used by Epping (1889) in connection with T2. Similar to Epping’s approach, Kugler appears to mean by this an effective translation that is primarily based on mathematical and astronomical interpretation. Inspection of his translation reveals that it is literal in the case of signs with a well-established meaning and also in terms of word order, but pragmatic and speculative for signs for which Assyriology could not yet offer a suitable meaning. Indeed, although Kugler’s Assyriological competence was more advanced than that of Epping, this did not help him very much in the case of the procedure texts, due to their stenographic and idiosyncratic terminology. Thus ‘boundary value’ is Kugler’s translation of ‘lib-bu-u’ (modern reading: lib₃-bu-u, ‘whereby’) and ‘obtained above’ is his translation of ‘mat gir’, which is nowadays read KUR-ad₂, ‘it reaches [an extremum]’. Other procedures from the same tablet are presented only in transliteration, because their terminology was still too inaccessible. Even though many signs are nowadays read or translated differently, Kugler’s algorithmic reconstructions are largely correct, but some of his astronomical interpretations later turned out to be wrong. This is not surprising, because the algorithms could be reconstructed by analyzing procedures and tables irrespective of their astronomical significance, which is rarely mentioned explicitly in the texts. There are numerous examples of algorithms that were reconstructed essentially correctly in this manner by Kugler and Epping before him, while their astronomical interpretation continued to be debated, sometimes until recently.⁵³

With BMR, Kugler established himself as the most authoritative and prolific scholar in the field of Babylonian astronomy. This position was solidified completely when, between 1907 and 1924, his magnum opus, Sternkunde und Sterndienst in Babel (SSB) (Astral Science and Astral Worship in Babylon) was published. This vast encyclopedic work of scholarship has a much wider scope than BMR, covering all corpora of Mesopotamian astral science of interest to Kugler. It consists of two rather different books. Book I, subtitled ‘The Development of Babylonian Planetary Science from its Beginnings until Christ. After Mostly Unpublished Sources of the British Museum’,⁵⁴ appeared in 1907. In spite of the title, this coherent monograph deals with Babylonian astronomical texts from the first millennium BCE, i.e. diaries and related texts and mathematical astronomy. Book II, which appeared in several installments between 1909 and 1924, deals with a wider range of texts about astronomy, astrology, divination and chronology from the second and the first millennia BCE. In the Preface to Book I Kugler justifies the wide scope of SSB as follows⁵⁵:

Certainly we must regret both aberrations of the human mind [polytheism and astrology], but a comforting thought can serve to soften our judgement. Astral religion was the noblest form of polytheism, and astrology even yielded large scientific benefits. Astral religion lifted the human heart from the bleakness of everyday life and purely material pleasure to a higher conception of life and it instructed him to recognize the majesty and the powerful rule of divinity in the radiance and world-encompassing movement of the stars. Moreover, astrology was the mother of astronomy, i.e. without the powerful conviction of a necessary connection between stellar constellation and human fate—if we momentarily disregard the sun and the moon as indicators of time—a scientific astronomy would hardly ever have been fostered in antiquity… Astral religion, astrology, astronomy (and chronology) form one whole in the celestial sciences of the Babylonians and, accordingly, the offices of priests and astrologers or calendar officials were united in a single person. What is connected historically can also be presented united in a single work, and in our case even more so, since a deeper understanding of the Babylonian religion can, often, be revealed only through astronomical investigations, naturally in conjunction with scholarship in language and religion.

While dutifully adding a rejection of polytheism and astrology, Kugler reveals that his approach to Babylonian astronomy was, in hindsight, quite modern. For him, all corpora of Babylonian astral science were interconnected, not only in terms of their subject matter but also because they were produced by the same actors. Note that Kugler made ample use of the concept of astral religion, even though he bitterly fought its Panbabylonian interpretation. Neither in BMR nor in SSB does Kugler consider it necessary to present a detailed justification of his research or define its place in the wider history of science, apart from repeating, like his predecessors, how much the tablets add to what is reported on Babylonian astronomy in the classical sources. It is rather clear that he considered Mesopotamian astral science in general and Babylonian astronomy in particular to be of sufficient interest on its own terms. However, from scattered remarks, such as the passage quoted above, one can infer that he was also of the opinion that his work on these topics would contribute to a better understanding of Mesopotamian religion and chronology. The preface continues with some considerations on the appropriate research methodology and editing practices for the astronomical texts⁵⁶:

However, a truly fruitful collaboration of such dissimilar sciences cannot at all be achieved through the principle of division of labor, or it can only with great difficulty. Surely the astronomer, supported only by the numbers in the astronomical cuneiform inscriptions, may succeed in clarifying certain technical expressions and thus provide the Assyriologist here und there with a handle for further investigations. Surely the Assyriologist may likewise succeed in transcribing and translating more or less correctly the most primitive astronomical observational reports and stereotypical omen formulas, so that they can be analysed astronomically. But even in the best case the results of joined forces cannot exceed that. Hence there is only one way out: the unification of linguistic and mathematical-astronomical knowledge in one and the same head, that is, either the Assyriologist decides to devote himself to mathematics and astronomy for a couple of years, or the astronomer to acquaint himself with language and mind of the Babylonians and the Assyrians. This is then what my efforts were aimed at for several years.

For Kugler, a scholar of Babylonian astronomy can be only be successful by mastering all the relevant disciplines like himself. In spite of this claim, Kugler continued to rely on Strassmaier and, as far as known, never copied or collated a cuneiform tablet in the British Museum. SSB Book I is nevertheless a mature piece of interdisciplinary scholarship with editions of tablets; commentaries; philological and astronomical analysis; a fourteen-page glossary; an index with the names of months, stars, planets, gods, kings, cities and persons; an astronomical index; a list of corrigenda; a list of tablets and, finally, copies of tablets.⁵⁷ Kugler’s editing practices have evolved in several ways. With the exception of mathematical astronomy (see below), most tablets are edited completely and without interruption, using a standardized arrangement with transliteration and translation placed on facing pages. Second, the rough and pragmatic ‘factual translations’ (Realübersetzungen) of BMR have given way to more accurate ‘translations’, which reflects Kugler’s increasing grasp of the technical terminology. Thirdly, Kugler adopts the typographical distinction between sumerograms and Akkadian phonetic signs also used by other Assyriologists: the former are written in capitals, the latter in small cursive letters. Fourthly, restorations are marked by square brackets rather than by a different font size. In his transliterations, Kugler continues to render as accurately as possible the Akkadian pronunciation of a text. Logograms are generally replaced by Akkadian normalized words, but they are now occasionally followed by the logogram in round brackets. Kugler still makes an exception for certain procedure texts, which he presents only in transliteration, followed by a commentary. His edition of the Jupiter procedure Rm 4, 431 (T4) is introduced as follows⁵⁸:

We first want to transcribe the text in a provisional manner by introducing phonetic writing instead of ideographic writing only when the correct reading is immediately obvious from the present investigation… Only after a complete decipherment and explanation has the time come for a phonetic representation (in as far as it is possible at all) and translation of the entire text. In order not to print the tablet twice, the restorations of parts destroyed or omitted by the scribe that turn out to be necessary are inserted in the transcription of the source between [ ] and the individual sentences are separated by ** (while no separator is noticable between sentences in the cuneiform text—be it an empty space or the occasionally used separator sign).

Kugler’s new convention with the asterisk (*) as a semantic separator, which has no counterpart in the cuneiform text, can be observed in the following lines of his transliteration of T4. On this occasion, he also introduces a new, ad hoc notation for damaged signs by placing vertical lines above them (as he explains in a footnote labeled β)⁵⁹ (Fig. 14.8).

Fig. 14.8

Transliterated lines from a procedure for Jupiter (Kugler 1907)

Book II of SSB appeared between 1909 and 1924 in three parts comprising a total of 630 pages. This last major work by Kugler is less coherent than the previous one and much more difficult to use, since it lacks any kind of index. The first two installments (1909, 1912) are devoted to celestial omens, astrology, meteorology and chronology, and therefore do not concern us here. However, note that the former begins with a section called ‘Retrospection to the First Book’ in which Kugler declares his definitive victory over the Panbabylonists by having demonstrated that Babylonian astronomy is a late development.⁶⁰ The third installment (1924)⁶¹ does include several editions of tablets with mathematical astronomy and astronomical diaries and related texts, but no copies, which were published much later by Schaumberger (1935). Also noteworthy are editions of two Babylonian horoscopes—a testimony to Kugler’s holistic view on Babylonian astral science.

That Kugler’s editing practices remained eclectic becomes especially clear in his edition of the normal star almanac Sp 1, 175 + Sp 2, 777 + 782 + 61 (Kugler 1912 = SSB II: 532–534).⁶² For reasons that remain unclear, this tablet is not edited in the usual format with a transliteration followed by a translation. Instead, Kugler produced a hybrid edition in which the planetary sections are translated, while the invocation and the lunar data are transliterated. Over the years, Kugler kept modifying his editing practices, but his transliterations of numbers remained consistent in that he always separated the digits by empty spaces. Furthermore, Kugler never took up Epping’s initiative to use modern graphs for representing Babylonian algorithms.

3 Johann Baptist Schaumberger

After Kugler’s death in 1929, Johann Baptist Schaumberger (1885–1955), a German Catholic priest of the order of the Redemptorists,⁶³ continued his unfinished work by writing a third supplement to SSB, which appeared in 1935. Schaumberger presents numerous new results of his own investigations of the tablets edited by Kugler in SSB Book II, and he includes Strassmaier’s hand copies of these tablets, as originally planned by Kugler. Schaumberger’s most significant accomplishment is his investigation of ‘SH 272’ (T1), which appears thirty-five years after the previous edition by Kugler (1900)⁶⁴:

Finally, I dared to investigate and present Kidinnu's large lunar table SH 272 in its full extent, including the final columns (computation of first crescent and last crescent) that were never dealt with before, Kidinnu's lunar computation is one of the biggest achievements of ancient astronomy.

The twenty-page edition⁶⁵ begins with an introduction in which Schaumberger summarizes the history of research on this tablet⁶⁶:

Since decades, work has been done on the decipherment of this famous tablet. Strassmaier copied the first fragments in 1879. Later he succeeded in reconstituting almost the entire tablet from many pieces. In the meantime, Epping had investigated the first pieces [Epping 1889]. That he was successful in explaining the text, in spite of its fragmentary state, is one of his most splendid accomplishments… The final columns, namely XIV and XVII, still resist interpretation. They will be investigated here. Kugler (1900: p. 12) published the largest part of the text (Cols. A until L = I until XI) in transcription. Appendices XV and XVI of this booklet offer the entire preserved cuneiform text for the first time. The autograph is based on the second copy of Strassmaier and on a photograph. The latter I owe to Mr. O. Neugebauer, who himself had the grace to collate the first ten columns with the photograph and produce a drawing demonstrating the connection between the different fragments of the tablet. For all that he is cordially thanked.

With Schaumberger, photographs of the tablets play an increasingly important role in research on Babylonian astronomy, but they are not yet included in his editions. Instead, Schaumberger offers a transcription and Strassmaier’s copy of T1. His edition is the first one to include all columns, but in terms of editing practices, it offers little change to the one by Kugler (1900). Some logograms (e.g. TAB, ‘add’, LAL, ‘subtract’ and those for the zodiacal signs) are replaced by modern symbols and restored text is printed in a different font but not enclosed in brackets. Remarkably, Schaumberger’s commentary includes a much more modern transliteration of a lunar table from the Louvre, AO (= Antiquités Orientales) 6491 (Schaumberger 1935: 387).⁶⁷ An enduring innovation concerns the nomenclature of the lunar columns. Schaumberger takes up a suggestion by Neugebauer to introduce a double designation for each column: first, a Roman numeral indicating its position on a given fragment; second, a capital letter that uniquely identifies its content.⁶⁸ The final appendix contains Neugebauer’s drawing of the arrangement of the fragments of T1, a reflection of Neugebauer’s awareness that a proper edition should include a full documentation of the material aspects of tablets (Fig. 14.9).

Fig. 14.9

Neugebauer’s drawing of T1 (obverse) in Schaumberger (1935)

Schaumberger’s supplement marks the end of a pioneering era that began with Epping and culminated in Kugler’s SSB, a monumental, Byzantine work covering all aspects of Mesopotamian astral science. After 1935, editing practices developed in a direction away from Kugler’s encyclopedic and eclectic style. Henceforth, different corpora of Mesopotamian astral science were investigated by different scholars and edited in separate monographs. Only in the 1990s, when the work of editing the various different corpora was nearing completion, have these divisions been softened due to a growing awareness of the connections between the different forms of astral science and a renewed interest in its social and institutional context—a development that Kugler would certainly approve of. Schaumberger continued to publish several papers on Mesopotamian astral science, but he never again worked on Babylonian mathematical astronomy, which had by then become the realm of Otto Neugebauer, who emerged as the translator and interpreter of this corpus by 1937.

4 Otto Neugebauer

Otto Neugebauer (1899–1990) ushered in a new phase in the historiography of Babylonian astronomy. Having recently published a complete edition of the Babylonian mathematical corpus (Neugebauer 1935–1937), Neugebauer switched his attention to Babylonian mathematical astronomy. Henceforth, the astronomical texts were edited as coherent text corpora. After making a brief appearance in Schaumberger (1935), his first publication on this topic was an admiring review of Schaumberger’s achievements (Neugebauer 1936). Since the methodology of Neugebauer’s research on Babylonian astronomy has been discussed elsewhere (Ossendrijver 2016), it suffices to recall some important features. One pillar of his research comprised various methods and tools for dating and reconstructing astronomical tables; a second one included his methods for reconstructing the underlying astronomical theories and empirical data. The production of critical editions was the third pillar of his research. The former two have in common that they largely consist of mathematical analysis. Especially in the early stages of his research, his focus lay squarely on the tabular texts with their sequences of numbers. A universalist mathematical perspective, which can be traced back to his mathematical education at Göttingen, underlies all of his investigations on ancient mathematical astronomy.⁶⁹ In a similar vein, Neugebauer frequently uses modern formulas and graphs in order to represent the Babylonian algorithms, unlike Kugler. Only later, when Neugebauer began to tackle the procedure texts, did the problem of translation attract his attention (see below). This contrasts with the more eclectic approach of Kugler, who, from the very beginning, combined the analysis of tables with efforts to translate procedure texts.

In a short programmatic paper (Neugebauer 1937) published in the newly founded journal Quellen and Studien (Sources and Studies), Neugebauer portrays the unsatisfactory state of publication of the astronomical texts. After decades of pioneering research, the modern reader is facing a forest of badly accessible monographs and papers, comprising layer upon layer of corrections on each tablet, with ever changing notations. He then announces the following ambitious plan⁷⁰:

I have decided … to make available the complete source material in a special text edition. I hope that, in this manner, approximately the same state of scientific methodology is reached in the field of pre-Greek mathematics and mathematical astronomy that has long ago become self-evident in the field of classical antiquity through the untiring efforts of Hultsch, Heiberg, Manitius, Tannery and many others, namely that one considers complete text editions to be the indispensible foundation of all further work.² [Footnote 2: For Egyptian mathematics there are the editions by Peet, Chace and Struve; for Babylonian, my edition.] This edition of the astronomical cuneiform texts of a mathematical character is part of a more comprehensive plan. The gentlemen L. Hartmann, J. Schaumberger and A. Schott and possibly other collaborators will also edit and publish the totality of the other classes of astronomical cuneiform texts, observational texts and astrological-astronomical texts, so that we finally hope to be able to present a truly complete collection of source materials on Babylonian astronomy. In the first part [‘Texts’] of this edition of the mathematical-astronomical cuneiform texts, which is in progress (I will henceforth simply cite it as MACT), I shall publish the entire textual material as completely as possible.

In a paper entitled ‘History of Ancient Astronomy: Methods and Problems’, published in 1946, Neugebauer reiterates some of the same points,

The most essential task is that of making the original sources accessible as easily as possible in their best available form. By the indefatigable work of Heiberg, Hultsch, Tannery and many others, we possess today a great part of the extant writings of the Greek scientists in excellent editions… To make Greek and Oriental source material more generally accessible, supplemented, of course, by modern translations and commentaries, will be the foremost problem of the future (Neugebauer 1946: 131).

For Neugebauer, it was clear that systematic research on Babylonian astronomy must proceed from complete editions of entire corpora produced in accordance with the same high standards that had been established in classical philology. The works of renowned historians of ancient Greek and Roman astronomy, mathematics and metrology⁷¹ serve as models for the edition that he was aiming for. Of the editions announced by Neugebauer, only the one that he intended to produce himself was actually realized within the decades after 1937. This became Astronomical Cuneiform Texts (ACT), which appeared in 1955. The other editions of the astronomical diaries and related texts and the astrological texts were not realized until after 1985 by a new generation of scholars. Neugebauer was a competent Assyriologist, but he relied on other Assyriologists to copy and collate tablets, not unlike Kugler. While continuing to work with the unpublished copies of Strassmaier, he also used the partly overlapping collection of copies produced by Theophilus Goldridge Pinches (1856–1934), who was subsequently assistant and curator of the cuneiform collection of the British Museum. These copies, produced between 1878 and 1900—at about the same time when Strassmaier was a regular visitor of the museum—were eventually published as Pinches and Sachs (1955). The latter author, the Assyriologist Abraham Sachs (1915–1983), became Neugebauer’s main collaborator in philological matters by 1941. Neugebauer was the first scholar of Babylonian astronomy to systematically use photographs of tablets along with the copies. This reflects the careful attention he gave to all physical aspects of the tablets. Virtually all of the editions by Neugebauer were based on copies by Strassmaier and Pinches, photographs that were sent to him by the British Museum, and various other collections and collations by Sachs and other fellow Assyriologists. Only few of these photographs were published in ACT or elsewhere.⁷²

Appearing some 18 years after Neugebauer’s announcement, ACT is the first ever edition of a complete corpus of astronomical texts and a milestone in editing practices. ACT is structured in a systematic manner, Vol. I being devoted to the moon, Vol. II to the planets, while Vol. III contains transliterations of the tabular texts as well as photographs and copies of selected tablets. Vol. I begins with an introduction about the history of research on Babylonian mathematical astronomy, documentary aspects of the tablets, colophons, mathematical methods, calendar issues, units and other general topics. The critical editions are preceded by introductory chapters about the algorithms that were reconstructed from the texts. In these chapters, Neugebauer typically combines a discussion of the Babylonian algorithms with explanations about the modern mathematical tools developed by him for reconstructing and analyzing these algorithms. By contrast, Neugebauer barely addresses editing practices, nor does he discuss his research methodology. His strongly mathematical approach is nevertheless immediately obvious in the introductory chapters, and various traces of it can be identified in the editions themselves. Within each section devoted to the moon or a planet, the tabular texts are always given priority, the procedure texts being edited in second position. All tablets are edited in their entirety, but not necessarily in the form of a single uninterrupted edition. If a tablet contains both tables and procedures, these different textual components are edited in separate chapters. Furthermore, both types of texts are edited differently. Each edition of a tabular text begins with basic documentary information⁷³ including a reference to the hand copy in Pinches and Sachs (1955), the transcription in Vol. III, followed by a critical apparatus and a commentary. The latter is usually divided into paragraphs, each devoted to a different column. For reasons of economy, no translations, hand copies or photographs of the tabular texts are included in ACT. Compared with the editions published by Kugler, who often mixed translation and transliteration, Neugebauer’s editions have a standardized and more modern appearance. However, they do contain mathematically motivated features that have no counterpart on the tablets. For instance, in columns with periodically varying number sequences, dashed, drawn and double horizontal rulings indicate where a minimum, maximum or zero crossing is reached, a notation introduced by Kugler (1900). Vertical rulings are drawn between all columns, even if they are not present on the tablet. Hence the tabular texts are transliterated in an idealized layout with added rulings that reflect the mathematical structure of the columns.

The editions of the procedure texts are arranged rather differently. Each one includes a transcription, a critical apparatus, a translation, a commentary and a reference to a hand copy, either in Pinches and Sachs (1955) or in Vol. III, and, usually, a photograph in Vol. III. Unlike the tabular texts, the tablets with procedures are not edited as coherent texts. Instead, each procedure is edited separately in the form of a transcription, critical apparatus, translation and commentary. By splitting up the texts in this manner, Neugebauer follows a practice initiated by Kugler (1900). Neugebauer’s editions of the procedure texts represent a tremendous step forward in our understanding of the highly technical astronomical and mathematical terminology. However, the translations are, in hindsight, quite strongly shaped by Neugebauer’s background in modern mathematics and astronomy. Arithmetical and astronomical terms are replaced by overly modern supposed equivalents, and semantic variations in the Babylonian terminology are not preserved in the translations (Ossendrijver 2016). A similar tendency underlies Neugebauer’s translations of Old Babylonian mathematical problem texts (Høyrup 1996). When editing procedure texts, Neugebauer did not aim for optimal semantic accuracy but for adequacy in a pragmatic, mathematical sense, in accordance with his universalist perspective on ancient astronomy.

Since Neugebauer, research on Babylonian astronomy has shifted its aims towards interpreting the Babylonian methods and practices and the underlying concepts in Babylonian terms rather than in modern terms. Moreover, the focus on reconstructing astronomical algorithms and the empirical data from which they were constructed is making way for a more holistic approach, whereby Babylonian astronomy is interpreted in its diverse institutional, political, religious and social contexts, while fully acknowledging the connections between the different forms of Babylonian astral science, including celestial divination and astrology.